Question: Determine how many solutions exist for the system of equations. ${-6x+y = -2}$ ${-2x+2y = 4}$
Explanation: Convert both equations to slope-intercept form: ${-6x+y = -2}$ $-6x{+6x} + y = -2{+6x}$ $y = -2+6x$ ${y = 6x-2}$ ${-2x+2y = 4}$ $-2x{+2x} + 2y = 4{+2x}$ $2y = 4+2x$ $y = 2+x$ ${y = x+2}$ Just by looking at both equations in slope-intercept form, what can you determine? ${y = 6x-2}$ ${y = x+2}$ The linear equations have different slopes. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ When two equations have different slopes, the lines will intersect once with one solution.